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Probabilistic models and related issues.


Apr
15
answered Invariant measure of Euler-Maruyama Discretisation of an Ito diffusion
Apr
4
answered Intuition on Lindeberg condition
Apr
2
awarded  Custodian
Apr
2
reviewed Approve suggested edit on Placing numbers $1,2,\ldots,n^3$ in a cube so that numbers of any two adjacent unit subcube are coprime
Apr
2
awarded  Citizen Patrol
Apr
1
answered Does $Mv$ converge to i.i.d in some sense?
Mar
7
awarded  Nice Answer
Feb
26
answered What are the difference between modeling with stochastic differential equations (SDE) and ordinary differential equations (ODE) with a random force?
Feb
26
revised Do Random Walks on the Hexagonal Lattice have a limit?
edited body
Feb
26
comment Do Random Walks on the Hexagonal Lattice have a limit?
1. Sort of, but not quite. If you are using the version of Donsker's theorem where you interpolate linearly between consecutive positions, then this interpolation applied to only odd (or only even) times will not coincide with your original process: you walk along the edges of the hexagonal lattice, but the new process walks along the edges of a certain triangular lattice. The difference between those processes is small and easy to estimate. 2. SAW is a very different beast. It is not a Markov process and, moreover, SAW of length $n$ is not a continuation of SAW of length $m$ for $n>m$.
Feb
25
answered Do Random Walks on the Hexagonal Lattice have a limit?
Feb
13
comment Approximation to the ratio of a Gaussian CDF to PDF
@domotorp: W.Feller. An Introduction to Probability Theory and its Applications, Vol I and II
Feb
13
comment Approximation to the ratio of a Gaussian CDF to PDF
The coefficients on the l.h.s. are chosen so that a certain cancellation occurs when you differentiate the l.h.s. of the second chain of inequalities.
Feb
13
comment Approximation to the ratio of a Gaussian CDF to PDF
@domotorp: I don't happen to have Feller's book anywhere around, but I do not see what seems to be a problem. Yes, the first line of inequalities is trivial, but it is only a differential version of the second one.
Jan
4
awarded  Yearling
Dec
20
comment A Claim on Typical Voronoi Cells
@MLT: I don't suffer from lack of publications, and this is hardly a way to advertise your project, so I am skeptical. If you think though your project is interesting, email me.
Dec
20
comment A Claim on Typical Voronoi Cells
@YoavKallus: your definition implies that $(x_i)_{i\ge 1}$ is a stationary process. This is bad. For instance, this will mean that there will be finite areas containing infinitely many points.
Dec
20
comment A Claim on Typical Voronoi Cells
@YoavKallus: If you try to define things precisely you will be in trouble or end up with meaningless statements. For example, what exactly do you mean by "the process is symmetric under relabelling"? In the construction of my answer I start with an arbitrary Poisson configuration and "relabel" it obtaining a labeling that violates the claim.
Dec
20
comment A Claim on Typical Voronoi Cells
I am afraid that my example shows that his claim is wrong.
Dec
20
comment A Claim on Typical Voronoi Cells
Answering your questions: 1)yes, this is a counterexample. 2) You want to average over all labelings, but on the plane there are infinitely many Poissonian points and infinitely many labelings on them, and there is no natural distribution on them. Of course, you can take a limit over boxes growing to infinity, then you will arrive at some notion of expected average cell size. Comparing individual points in this scheme will not work, their individuality will be lost in the averaging procedure.